1. Technical Field
This disclosure relates to medical imaging, including positron emission tomography (PET) scanners which produce and process time-of-flight (TOF) information.
2. Description of Related Art
PET scanners may be used for both biomedical and neuroscientific research and clinical studies for diagnosing and staging disease and for assessing response to therapy.
PET scans may be taken to produce 3D images of various biological processes and functions within a living body. A patient may by injected with a radiotracer. The radiotracer may include biochemical molecules that participate in the physiological process. The biochemical molecules may be tagged with a positron emitting radioisotope. These radioisotopes may naturally decay inside the body, ejecting positron particles from their nuclei.
Each emitted positron may quickly combine with an electron, which may then annihilate one another. The annihilation event may produce a pair of gamma photons traveling in opposite directions. The gamma photons may be detected by two detectors in an array of detectors positioned around the patient.
The simultaneous detection of a gamma photon by two different detectors in the array may be indicative of a single annihilation event. The annihilation may be assumed to have taken place at some point on the line between the two detectors which have simultaneously detected the gamma photons. This connecting line is commonly referred to as a “line of response” (LOR).
Several annihilation events may take place on the same LOR. The number of detected annihilation events on each possible LOR may be counted and stored, along with information identifying the spatial coordinates of the LOR. This collective set of data is commonly referred to as a sinogram.
The detector array may be a single ring of detectors, commonly referred to as a 2D detector array, such as is illustrated in FIG. 1 (taken from U.S. Pat. No. 7,381,959). The detector may instead include several rings of detectors stacked in a cylinder, commonly referred to as a 3D detector array, such as is illustrated in FIG. 2. (also taken from U.S. Pat. No. 7,381,959).
A 2D detector array may only detect annihilation events which produce an LOR which is perpendicular to the axis of the array, such as LORs 101 and 103 in FIG. 1. A 3D detector array, such as the one shown in FIG. 2, on the other hand, may also detect annihilation events which produce LORs which are not perpendicular to the axis of the array, such as LOR 201.
A 3D image showing the location of tagged biochemical molecules within a body may be reconstructed from the sinogram data. This may be accomplished by transforming the LOR data into a 3D image of the annihilation events using complex mathematical computations. This transformation process is known as image reconstruction. Image reconstruction may be based on Fourier transform relationships between the 3D image and the sinogram data. Image reconstruction may instead be based on physical and statistical models of the photon pair detection process that use computational numerical optimization methods to produce the best possible image based on these models.
Most annihilation events may not produce LORs which are perpendicular to the axis of the detector array. Thus, 2D detector arrays produce far less data than 3D detector arrays. This smaller data set may be easier to process, but may result in poorer quality 3D images. The 3D data sets may be able to produce better image quality through increased efficiency in detecting annihilation events leading to an improved signal-to-noise ratio in the sinogram data.
Much of the additional image clarity provided by 3D PET scan data may be preserved, without performing intensive data computations during the reconstruction process, by first converting the 3D PET scan data into 2D PET scan data before the 3D image is reconstructed. This has been done by taking the Fourier transform with respect to the spatial coordinates of the LORs in the 3D PET scan data in a process known as “Fourier rebinning” See Defrise M., Kinahan P. E., Townsend D. W., Michel C., Sibomana M., and Newport D. F. (1997), “Exact and Approximate Rebinning Algorithms for 3-D PET data,” IEEE Trans. Med. Imaging, vol. 16, pp. 145-158 and Liu X., Defrise M., Michel C., Sibomana M., Comtat C., Kinahan P., and Townsend D. (1999), “Exact Rebinning Methods for Three-Dimensional PET,” IEEE Trans. Med. Imaging, vol. 18, pp. 657-664.
The quality of reconstructed 3D images may be further enhanced by detecting and storing the difference in time between the arrivals of each pair of gamma photons from each annihilation event. This is commonly referred to as “time of flight” (TOF) information. A TOF of zero, for example, indicates that the annihilation event took place at approximately the midpoint of the LOR. A positive or negative TOF, on the other hand, indicates that the annihilation event took place to the left or right of this midpoint.
Fully 3D time-of-flight (TOF) PET scanners may offer the potential for previously unachievable signal-to-noise ratio in clinical PET. Recent developments of fast scintillators such as LSO and LaBr3 make clinical TOF PET practical. However, fully 3D TOF PET image reconstruction using accurate system and noise models may be challenging due to the huge data size.
Efforts have been made to reduce data size without losing information, a process commonly referred to as “rebinning.”
One approach to rebinning of TOF data is single slice rebinning (SSRB-TOF). See Mullani N., Wong W., Hartz R., Philippe E., and Yerian K. (1982) “Sensitivity Improvement of TOFPET by the Utilization of the Inter-Slice Coincidence,” IEEE Trans. Nucl. Sci., vol. 29, pp. 479-483. Oblique TOF sinograms are combined to form a set of stacked 2D TOF sinograms in a similar manner to single slice rebinning for non TOF data. This method may reduce achievable image resolution through the rebinning procedure.
As an alternative to SSRB-TOF is an approximate Fourier rebinning method in which the rebinning is performed in the Fourier domain See U.S. Pat. No. 7.417,231 B2 US Patent; Defrise M., Casey M. E., Michel C., and Conti M. (2005), “Fourier Rebinning of Time-of-Flight PET Data,” Phys. Med. Biol., vol. 50, pp. 2749-2763. This approximate approach may show improved performance over SSRB-TOF by making use of the Fourier transform properties of the TOF sinograms. The data is rebinned from 3D TOF to stacked 2D TOF sinograms.
An exact rebinning equation was derived based on a consistency condition expressed by a partial differential equation in the continuous data domain. See Defrise M., Panin V., Michel C., and Casey M. E. (2008), “Continuous and Discrete Data Rebinning in Time-of-Flight PET,” IEEE Trans. Med. Imaging, vol. 27, pp. 1310-1322; U.S. PGPub 2008/0099686, where rebinning is performed with respect to the axial variables. This result motivated the development of an approximate discrete axial rebinning method. In this method, a cost function based on a bias and variance tradeoff is used to find optimal pre-computable rebinning coefficients. Using these coefficients, a weighted average of the axial lines of response is taken to estimate an appropriate line of response in a 2D direct plane. The exact mappings that rebin 3D TOF data to 2D TOF data require calculation of partial derivatives which are numerically unstable and may lead to poor results when used with noisy data. Both the exact and approximate rebinning methods are again restricted to rebinning to stacked 2D TOF data.
All the rebinning methods described above rebin 3D TOF data to 2D TOF data and retain the TOF component in the rebinned data. As a result, the reconstruction methods and computer programs that are used to compute the 3D PET images must work directly with the TOF data.